CN113962612A - Electric heating combined system distribution robust optimization scheduling method based on improved Wasserstein measure - Google Patents

Electric heating combined system distribution robust optimization scheduling method based on improved Wasserstein measure Download PDF

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CN113962612A
CN113962612A CN202111417104.9A CN202111417104A CN113962612A CN 113962612 A CN113962612 A CN 113962612A CN 202111417104 A CN202111417104 A CN 202111417104A CN 113962612 A CN113962612 A CN 113962612A
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刘鸿鹏
李宏伟
张伟
张书鑫
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Northeast Electric Power University
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Northeast Dianli University
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06F30/15—Vehicle, aircraft or watercraft design
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    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
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Abstract

An electric heating combined system distribution robust optimization scheduling method based on improved Wasserstein measure relates to the technical field of renewable energy scheduling in an electric heating combined system. The method aims to solve the problem that an uncertainty set constructed by the traditional Wasserstein measure theoretically contains infinite probability distributions, and influences the solving efficiency of an optimized scheduling model; and the uncertainty modeling method for the electric automobile cluster in the electric-heat combined system is limited to a probability distribution function and cannot meet the multi-scenario scheduling requirement. The method comprises the steps of constructing an uncertain set of wind power prediction errors, introducing extreme situation indexes of wind power output power into the uncertain set of wind power prediction errors, establishing the uncertain set of wind power prediction errors in an extreme scene, respectively constructing uncertain sets of electric vehicle operating characteristics in a charging state and a discharging state, and finally establishing a distributed robust optimization scheduling model in the uncertain sets.

Description

Electric heating combined system distribution robust optimization scheduling method based on improved Wasserstein measure
Technical Field
The invention belongs to the technical field of renewable energy scheduling in an electric heating combined system.
Background
Aiming at the problem of uncertainty optimization of renewable energy sources in an electric heating combined system, the distributed robust optimization method can well avoid the defects of poor economy and high conservation existing in the process of processing the uncertainty problem of random optimization and robust optimization. However, modeling the uncertainty set of the distributed robust optimization problem has been a key difficulty for the distributed robust optimization model.
The uncertainty set construction based on Wasserstein measure makes up the defects of the probability distribution function and KL (Kullback-Leibler) divergence in the uncertainty set construction. However, the uncertainty set constructed by the conventional Wasserstein measurement theoretically contains infinite probability distributions, which seriously affects the solution efficiency of the optimized scheduling model. Meanwhile, an uncertainty modeling method for an electric vehicle cluster in an electric-heat combined system is limited to a probability distribution function and is difficult to meet the actual multi-scenario scheduling requirement.
Disclosure of Invention
The method aims to solve the problem that an uncertainty set constructed by the traditional Wasserstein measure theoretically contains infinite probability distributions, and influences the solving efficiency of an optimized scheduling model; and the uncertainty modeling method for the electric vehicle cluster in the electric heating combined system is limited to a probability distribution function and cannot meet the multi-scene scheduling requirement, so that an electric heating combined system distribution robust optimization scheduling method based on an improved Wasserstein measure is provided.
An electric heating combined system distribution robust optimization scheduling method based on improved Wasserstein measure comprises the following steps:
the method comprises the following steps: construction of uncertain set of wind power prediction errors
Figure BDA0003375650730000011
The indeterminate set
Figure BDA0003375650730000012
To be distributed empirically
Figure BDA0003375650730000013
As center of circle, epsilonwWasserstein sphere, radius, expression is as follows:
Figure BDA0003375650730000014
wherein the content of the first and second substances,
Figure BDA0003375650730000015
is a predicted value of the wind power output power,
Figure BDA0003375650730000016
is the set of all probability distributions xi with support,
Figure BDA0003375650730000017
is a true distribution
Figure BDA0003375650730000018
Is a desired value of (a), wherein
Figure BDA0003375650730000019
Figure BDA00033756507300000110
In the form of a euclidean norm,
Figure BDA00033756507300000111
is a true distribution
Figure BDA00033756507300000112
And empirical distribution
Figure BDA00033756507300000113
Combined probability distribution of (xi)wAnd
Figure BDA00033756507300000114
are respectively true distribution
Figure BDA00033756507300000115
And empirical distribution
Figure BDA00033756507300000116
And respectively obey
Figure BDA00033756507300000117
And
Figure BDA00033756507300000118
inf (·) is an infimum function;
step two: extreme scene indexes of wind power output power are introduced into uncertain sets of wind power prediction errors, and the uncertain sets of the wind power prediction errors in extreme scenes are established
Figure BDA0003375650730000021
Figure BDA0003375650730000022
Wherein alpha is1And alpha2The percentage of allowable upward and downward fluctuations of the wind power prediction error,
Figure BDA0003375650730000023
and
Figure BDA0003375650730000024
threshold values for ramp up and ramp down power, respectively;
step three: respectively constructing uncertain sets of the running characteristics of the electric automobile in a charging state and a discharging state,
uncertainty set of electric vehicle operating characteristics under charging state
Figure BDA0003375650730000025
Comprises the following steps:
Figure BDA0003375650730000026
wherein, Pt CharIs the total charging power, P, of the electric vehicle in the charging state at the moment tt PrecharFor the predicted charging power, P, of the electric vehicle in the charging state at time tt UpcharAnd Pt DowncharThe maximum fluctuating charging power of the electric automobile in the charging state at the moment t and the maximum fluctuating charging power of the electric automobile in the charging state at the moment t are respectively,
Figure BDA0003375650730000027
and
Figure BDA0003375650730000028
all variables are 0 to 1,
Figure BDA0003375650730000029
And is
Figure BDA00033756507300000210
Figure BDA00033756507300000211
Is the regulation coefficient of the electric vehicle in the charging state, and
Figure BDA00033756507300000212
Figure BDA00033756507300000213
Figure BDA00033756507300000214
t is a total scheduling period;
uncertainty set of electric automobile running characteristics in discharging state
Figure BDA00033756507300000215
Comprises the following steps:
Figure BDA00033756507300000216
wherein, Pt DisIs the total discharge power, P, of the electric vehicle in the discharge state at the moment tt PredisPredicted discharge power, P, of an electric vehicle in the discharge state at time tt UpdisAnd Pt DowndisThe maximum fluctuating discharge power of the electric automobile in the discharge state at the moment t respectively upwards and downwards,
Figure BDA00033756507300000217
and
Figure BDA00033756507300000218
all variables are 0 to 1,
Figure BDA00033756507300000219
And is
Figure BDA00033756507300000220
Figure BDA00033756507300000221
Is the regulation coefficient of the electric automobile in the discharge state, and
Figure BDA00033756507300000222
Figure BDA00033756507300000223
Figure BDA00033756507300000224
step four: establishing a distributed robust optimization scheduling model under an uncertain set:
Figure BDA00033756507300000225
wherein the content of the first and second substances,
Figure BDA0003375650730000031
in order to reduce the running cost of the conventional unit,
Figure BDA0003375650730000032
for the output power of the ith conventional unit at time t,
Figure BDA0003375650730000033
and
Figure BDA0003375650730000034
starting and stopping state quantities of a conventional unit, respectively, when starting the conventional unit
Figure BDA0003375650730000035
When the conventional unit is stopped
Figure BDA0003375650730000036
Figure BDA0003375650730000037
In order to account for the fuel costs of the cogeneration unit,
Figure BDA0003375650730000038
is the power output value of the cogeneration unit,
Figure BDA0003375650730000039
in order to reduce the cost of the electric automobile,
Figure BDA00033756507300000310
and
Figure BDA00033756507300000311
charging power and discharging power respectively for the nth electric vehicle at time t, NGTotal number of conventional units, NCHPTotal number of cogeneration units, NEVIs the total number of the electric automobiles,
Figure BDA00033756507300000312
for the total indeterminate set of the cogeneration system,
Figure BDA00033756507300000313
EP[i]is composed of
Figure BDA00033756507300000314
The expected value of any one of the distributions P,
Figure BDA00033756507300000315
wherein x is the output power adjustment value set of the conventional unit and the cogeneration unit,
Figure BDA00033756507300000316
a fluctuation value set C of wind power prediction error and electric vehicle charge and discharge powerEVRIn order to reduce the replacement cost of the battery of the electric automobile,
Figure BDA00033756507300000317
is the total charge and discharge capacity of the nth electric vehicle battery,
Figure BDA00033756507300000318
and
Figure BDA00033756507300000319
power fluctuation values of the electric vehicle in the charging state and the discharging state, cG,iAnd cCHP,iAdjusting cost coefficients for output power of the ith conventional unit and the ith cogeneration unit respectively,
Figure BDA00033756507300000320
and
Figure BDA00033756507300000321
the participation coefficients, delta P, of the ith conventional unit and the ith cogeneration unit at the moment tt GAnd Δ Pt CHPRespectively the regulated power of the conventional unit and the cogeneration unit.
Further, according to historical wind power predictionPower error data set
Figure BDA00033756507300000322
Building an empirical distribution
Figure BDA00033756507300000323
Figure BDA00033756507300000324
Where N is the total number of historical samples, j is 1, 2., N,
Figure BDA00033756507300000325
predicting power error data for jth historical wind power
Figure BDA00033756507300000326
Dirac measure of.
Further, the above Euclidean norm
Figure BDA00033756507300000327
The expression of (a) is as follows:
Figure BDA00033756507300000328
further, the extreme scenario in step two above includes the following two cases:
the first is that the wind power output power is the maximum value or the minimum value, and then the maximum wind power output power at the moment t
Figure BDA00033756507300000329
And minimum wind power output
Figure BDA00033756507300000330
The expression of (a) is:
Figure BDA0003375650730000041
wherein the content of the first and second substances,
Figure BDA0003375650730000042
the predicted value of the wind power output power at the moment t is obtained;
the second is that the climbing power of the wind power exceeds the threshold value, and the extreme climbing power of the wind power in the time interval (t, t + Δ t) is:
Figure BDA0003375650730000043
wherein the content of the first and second substances,
Figure BDA0003375650730000044
and
Figure BDA0003375650730000045
up and down power of wind power, P, respectivelyw,tAnd Pw,t+ΔtThe output power of the wind power is respectively at t moment and t + delta t moment, and delta t is time increment.
Further, the electric vehicle in a charged state with a state of charge of 20% or less and the electric vehicle in a discharged state with a state of charge of 80% or more are described above.
Further, the running cost of the above conventional unit
Figure BDA0003375650730000046
Including fuel costs and start-stop costs.
According to the electric-heat combined system distribution robust optimization scheduling method based on the improved Wasserstein measure, wind power prediction errors and extreme wind power output scenes are comprehensively considered, the solving efficiency of an optimization scheduling model of the system can be effectively improved, the operation economy of the system is improved, and the multi-scene scheduling requirements are met.
Drawings
FIG. 1 is an IEEE 9 node combined heat and power system;
FIG. 2 shows the operation of the electric vehicle in scenarios 2 and 3;
FIG. 3 shows the adjustment amounts of the CON and CHP units;
FIG. 4 is a flow chart of an improved Wasserstein measure-based electric-thermal combined system distribution robust optimization scheduling method.
Detailed Description
The first embodiment is as follows: specifically, the present embodiment is described with reference to fig. 1 to fig. 4, and the improved Wasserstein measure-based robust optimization scheduling method for distribution of an electric-thermal combined system in the present embodiment includes the following steps:
the method comprises the following steps: using empirical distributions
Figure BDA0003375650730000047
Estimating a true distribution as a reference distribution
Figure BDA0003375650730000048
Specifically, the power error data set is predicted according to historical wind power
Figure BDA0003375650730000049
Building an empirical distribution
Figure BDA00033756507300000410
The empirical distribution
Figure BDA00033756507300000411
Is a step function, and the expression is:
Figure BDA00033756507300000412
where N is the total number of historical samples, j is 1, 2., N,
Figure BDA00033756507300000413
predicting power error data for jth historical wind power
Figure BDA00033756507300000414
Dirac measure of.
According to the law of large numbers, it can be shown that,when more data is available, reference distribution
Figure BDA0003375650730000051
Will certainly converge to the true distribution gradually
Figure BDA0003375650730000052
Then an uncertain set of wind power prediction errors is constructed
Figure BDA0003375650730000053
The indeterminate set
Figure BDA0003375650730000054
To be distributed empirically
Figure BDA0003375650730000055
As center of circle, epsilonwWasserstein sphere, radius, expression is as follows:
Figure BDA0003375650730000056
wherein the content of the first and second substances,
Figure BDA0003375650730000057
is a predicted value of the wind power output power,
Figure BDA0003375650730000058
is the set of all probability distributions xi with support,
Figure BDA0003375650730000059
is a true distribution
Figure BDA00033756507300000510
Is a desired value of (a), wherein
Figure BDA00033756507300000511
Figure BDA00033756507300000512
In the form of a euclidean norm,
Figure BDA00033756507300000513
is a true distribution
Figure BDA00033756507300000514
And empirical distribution
Figure BDA00033756507300000515
Combined probability distribution of (xi)wAnd
Figure BDA00033756507300000516
are respectively true distribution
Figure BDA00033756507300000517
And empirical distribution
Figure BDA00033756507300000518
And respectively obey
Figure BDA00033756507300000519
And
Figure BDA00033756507300000520
inf (·) is an infimum function.
Step two: the distribution robust optimization scheduling model based on the Wasserstein measure can make up the defects of other uncertain sets such as cumulative probability distribution, KL divergence and the like. However, as the sample set size increases, the amount of computation also increases dramatically. Meanwhile, the distributed robust optimal scheduling tries to make the best decision under the condition of the worst probability distribution, thereby ensuring a decision scheme of all possible probability distributions in an uncertain set. Therefore, under the worst case probability distribution, the robustness of the distributed robust optimized scheduling can be ensured.
Based on the facts, the wind power extreme situation indexes are established, and the worst probability distribution set of the wind power output needs to be screened out as much as possible so as to improve the calculation efficiency of the distributed robust optimization scheduling; without losing the robustness and economy of the decision-making scheme. At present, there are two extreme wind power output power scenarios:
the first is that the wind power output power is the maximum value or the minimum value, and then the maximum wind power output power at the moment t
Figure BDA00033756507300000521
And minimum wind power output
Figure BDA00033756507300000522
The expression of (a) is:
Figure BDA00033756507300000523
wherein the content of the first and second substances,
Figure BDA00033756507300000524
and the predicted value of the wind power output power at the moment t is obtained.
The second is that the climbing power of the wind power exceeds the threshold value, and the extreme climbing power of the wind power in the time interval (t, t + Δ t) is:
Figure BDA0003375650730000061
wherein the content of the first and second substances,
Figure BDA0003375650730000062
and
Figure BDA0003375650730000063
up and down power of wind power, P, respectivelyw,tAnd Pw,t+ΔtThe output power of the wind power is respectively at t moment and t + delta t moment, and delta t is time increment.
Extreme scenario indexes of wind power output power are introduced into uncertain sets of wind power prediction errors, so that the uncertain sets of the wind power prediction errors in extreme scenes are established
Figure BDA0003375650730000064
Figure BDA0003375650730000065
Wherein alpha is1And alpha2The percentage of allowable upward and downward fluctuations of the wind power prediction error,
Figure BDA0003375650730000066
and
Figure BDA0003375650730000067
threshold values for ramp up and ramp down power, respectively.
Step three: unlike wind power generation, which is greatly affected by meteorological factors, the operating characteristics of electric vehicles can be controlled by directing the electric vehicles to charge or discharge in order. In addition, in the future, more and more electric vehicles are connected to a power grid, and reasonable and effective control is necessary. By appropriate adjustment, the uncertainty of the electric vehicle cluster can be greatly reduced. However, while the orderly regulation attenuates the uncertainty of the electric vehicle cluster, the uncertainty of the electric vehicle cluster still exists. Therefore, an uncertainty set of the electric vehicle cluster under the ordered control needs to be established.
Electric vehicles are classified into three types according to the difference of the electric vehicle charge state:
1) electric Vehicles (CSEVs) in a state of charge of 20% or less;
2) electric Vehicles (DSEVs) in a discharge state with a state of charge of 80% or more;
3) and the state of charge of more than 20% and less than 80% is mobile energy storage type electric vehicles (MSEVs).
Here only the uncertainties of CSEVs and DSEVs are considered and MSEVs are considered reserve resources.
Respectively constructing uncertain sets of the running characteristics of the electric automobile in a charging state and a discharging state,
uncertainty of electric vehicle operating characteristics under charging conditionsSet of definite degree
Figure BDA0003375650730000068
Comprises the following steps:
Figure BDA0003375650730000069
wherein, Pt CharIs the total charging power, P, of the electric vehicle in the charging state at the moment tt PrecharFor the predicted charging power, P, of the electric vehicle in the charging state at time tt UpcharAnd Pt DowncharThe maximum fluctuating charging power of the electric automobile in the charging state at the moment t and the maximum fluctuating charging power of the electric automobile in the charging state at the moment t are respectively,
Figure BDA0003375650730000071
and
Figure BDA0003375650730000072
all variables are 0 to 1,
Figure BDA0003375650730000073
And is
Figure BDA0003375650730000074
Figure BDA0003375650730000075
The regulation coefficient of the electric vehicle in the charging state (the value of the charging power of the electric vehicle in the charging state in the dispatching period reaching the fluctuation interval boundary value) is obtained, and
Figure BDA0003375650730000076
Figure BDA0003375650730000077
Figure BDA0003375650730000078
and T is the total scheduling period.
Uncertainty of electric vehicle operating characteristics in discharge stateDegree set
Figure BDA0003375650730000079
Comprises the following steps:
Figure BDA00033756507300000710
wherein, Pt DisIs the total discharge power, P, of the electric vehicle in the discharge state at the moment tt PredisPredicted discharge power, P, of an electric vehicle in the discharge state at time tt UpdisAnd Pt DowndisThe maximum fluctuating discharge power of the electric automobile in the discharge state at the moment t respectively upwards and downwards,
Figure BDA00033756507300000711
and
Figure BDA00033756507300000712
all variables are 0 to 1,
Figure BDA00033756507300000713
And is
Figure BDA00033756507300000714
Figure BDA00033756507300000715
Is the regulation coefficient of the electric automobile in the discharge state, and
Figure BDA00033756507300000716
Figure BDA00033756507300000717
Figure BDA00033756507300000718
step four: in order to comprehensively consider the uncertainty of the wind power and electric vehicle cluster, a distributed robust optimization scheduling model under an uncertain set needs to be established, and the model is divided into two stages.
In the first stage, a unit output power plan is arranged according to the predicted output values of the wind power, the electric automobile charging power and the discharging power, and the sum of the power generation cost, the start-stop cost, the electric automobile running cost and the expected cost in the second stage is minimized. The concrete formula is as follows:
Figure BDA00033756507300000719
wherein the content of the first and second substances,
Figure BDA00033756507300000720
the running cost of the conventional unit comprises the fuel cost and the start-stop cost,
Figure BDA00033756507300000721
for the output power of the ith conventional unit at time t,
Figure BDA00033756507300000722
and
Figure BDA00033756507300000723
starting and stopping state quantities of a conventional unit, respectively, when starting the conventional unit
Figure BDA00033756507300000724
When the conventional unit is stopped
Figure BDA00033756507300000725
In order to account for the fuel costs of the cogeneration unit,
Figure BDA00033756507300000726
is the power output value of the cogeneration unit,
Figure BDA00033756507300000727
in order to reduce the cost of the electric automobile,
Figure BDA00033756507300000728
and
Figure BDA00033756507300000729
charging power and discharging power respectively for the nth electric vehicle at time t, NGTotal number of conventional units, NCHPTotal number of cogeneration units, NEVIs the total number of the electric automobiles,
Figure BDA00033756507300000730
for the total indeterminate set of the cogeneration system,
Figure BDA00033756507300000731
EP[·]is composed of
Figure BDA00033756507300000732
The expected value of any one of the distributions P.
And in the second stage, the fluctuation of the wind power generation and the electric vehicle charge and discharge power is adjusted, the objective function of the fluctuation of the wind power generation and the electric vehicle charge and discharge power comprises the adjusting cost of a generator set and the running cost of the electric vehicle, and the specific formula is as follows:
Figure BDA0003375650730000081
wherein x is the output power adjustment value set of the conventional unit and the cogeneration unit,
Figure BDA0003375650730000082
a fluctuation value set C of wind power prediction error and electric vehicle charge and discharge powerEVRIn order to reduce the replacement cost of the battery of the electric automobile,
Figure BDA0003375650730000083
is the total charge and discharge capacity of the nth electric vehicle battery,
Figure BDA0003375650730000084
and
Figure BDA0003375650730000085
power fluctuation values of the electric vehicle in the charging state and the discharging state, cG,iAnd cCHP,iAdjusting cost coefficients for output power of the ith conventional unit and the ith cogeneration unit respectively,
Figure BDA0003375650730000086
and
Figure BDA0003375650730000087
the participation coefficients, delta P, of the ith conventional unit and the ith cogeneration unit at the moment tt GAnd Δ Pt CHPRespectively the regulated power of the conventional unit and the cogeneration unit.
In order to verify the effectiveness of the electric heating combination system distribution robust optimization scheduling method based on the improved Wasserstein measure, simulation verification is carried out on an improved IEEE 9 node electric heating combination system, and the IEEE 9 node electric heating combination system is shown in figure 1.
Three scheduling scenarios are considered to analyze the influence of wind power uncertainty and Electric Vehicle (EV) running characteristic uncertainty on the scheduling result based on the extreme scenarios. The three scheduling scenarios are as follows:
scenario 1: a scheduling scheme under a basic condition is considered, and the scheme only considers a robust optimization model of the distribution of the electric heating combined system based on Wasserstein measurement.
Scenario 2: compared with the scheduling scene 1, the electric heating combined system distribution robust optimization model of the Wasserstein measure is improved under the condition of considering extreme wind power.
Scenario 3: compared with the dispatching scheme 2, the electric heating combined system distribution robust optimization model considering the uncertainty of the running characteristics of the electric automobile is also provided.
1) Comparative analysis of results for scenario 1 and scenario 2
By comparing the scheduling scenes 1 and 2, the effectiveness and superiority of the distribution robust optimization scheduling model based on the improved Wasserstein measure are verified. Table 1 gives the running costs and computation times of the optimized scheduling models for scenario 1 and scenario 2.
The results shown in table 1 indicate that the operation cost of the optimized scheduling model of the scene 2 is close to that of the optimized scheduling model of the scene 1, and even smaller than that of the optimized scheduling model of the scene 1, which proves the effectiveness of the proposed optimized scheduling model of the scene 2 and has better economical efficiency. In addition, the scenario 2 optimized scheduling model has great advantage in computation time. As can be seen from Table 1, the computation time gap between the two models increases dramatically when more historical data is available. Taking the simulation result sampled 5000 times as an example, the proposed optimal scheduling model of scenario 2 is 73.88% faster in calculation speed than the optimal scheduling model of scenario 1.
Table 1 comparison of results for scene 1 and scene 2
Figure BDA0003375650730000091
2) Comparative analysis of results for scene 2 and scene 3
The influence of uncertainties in the operating behavior of the electric vehicle on the optimization results can be explained here. The running costs and computation times for scenario 2 and scenario 3 are compared as shown in table 2. The electric vehicle operation conditions of the scenarios 2 and 3 are shown in fig. 2. The regulated power of CON (conventional unit) and CHP (cogeneration unit) is shown in fig. 3. As can be seen from table 2, the total operating cost of scenario 3 is higher than the operating cost of scenario 2 due to the uncertainty of the operating characteristics of the electric vehicle, and especially the depreciation cost of the electric vehicle battery is higher than 30.45% of scenario 2.
Table 2 comparison of scene 2 and scene 3
Figure BDA0003375650730000092
As can be seen from fig. 2, the electric vehicle charging power and discharging power of scenario 3 are greater than the operating conditions of scenario 2. This is because the uncertainty of the electric vehicle increases, causing the charging power and the discharging power of the MSEVs to vary to cope with fluctuations of the CSEVs and the DSEVs. As shown in fig. 3, the CON and CHP crew also participate in the adjustment to account for EV uncertainty. The CHP unit is the main conditioning unit, since the adjustment cost of the CHP unit is lower than that of the CON unit.

Claims (6)

1. An electric heating combined system distribution robust optimization scheduling method based on improved Wasserstein measure is characterized by comprising the following steps:
the method comprises the following steps: construction of uncertain set of wind power prediction errors
Figure FDA0003375650720000011
The indeterminate set
Figure FDA0003375650720000012
To be distributed empirically
Figure FDA0003375650720000013
As center of circle, epsilonwWasserstein sphere, radius, expression is as follows:
Figure FDA0003375650720000014
wherein the content of the first and second substances,
Figure FDA0003375650720000015
is a predicted value of the wind power output power,
Figure FDA0003375650720000016
is the set of all probability distributions xi with support,
Figure FDA0003375650720000017
is a true distribution
Figure FDA0003375650720000018
Is a desired value of (a), wherein
Figure FDA0003375650720000019
Figure FDA00033756507200000110
In the form of a euclidean norm,
Figure FDA00033756507200000111
is a true distribution
Figure FDA00033756507200000112
And empirical distribution
Figure FDA00033756507200000113
Combined probability distribution of (xi)wAnd
Figure FDA00033756507200000114
are respectively true distribution
Figure FDA00033756507200000135
And empirical distribution
Figure FDA00033756507200000115
And respectively obey
Figure FDA00033756507200000116
And
Figure FDA00033756507200000117
inf (·) is an infimum function;
step two: extreme scene indexes of wind power output power are introduced into uncertain sets of wind power prediction errors, and the uncertain sets of the wind power prediction errors in extreme scenes are established
Figure FDA00033756507200000118
Figure FDA00033756507200000119
Wherein alpha is1And alpha2The percentage of allowable upward and downward fluctuations of the wind power prediction error,
Figure FDA00033756507200000120
and
Figure FDA00033756507200000134
threshold values for ramp up and ramp down power, respectively;
step three: respectively constructing uncertain sets of the running characteristics of the electric automobile in a charging state and a discharging state,
uncertainty set of electric vehicle operating characteristics under charging state
Figure FDA00033756507200000121
Comprises the following steps:
Figure FDA00033756507200000122
wherein the content of the first and second substances,
Figure FDA00033756507200000123
for the total charging power of the electric vehicle in the charging state at the time t,
Figure FDA00033756507200000124
for the predicted charging power of the electric vehicle in the charging state at time t,
Figure FDA00033756507200000125
and
Figure FDA00033756507200000126
the maximum fluctuating charging power of the electric automobile in the charging state at the moment t and the maximum fluctuating charging power of the electric automobile in the charging state at the moment t are respectively,
Figure FDA00033756507200000127
and
Figure FDA00033756507200000128
all variables are 0 to 1,
Figure FDA00033756507200000129
And is
Figure FDA00033756507200000130
Figure FDA00033756507200000131
Is the regulation coefficient of the electric vehicle in the charging state, and
Figure FDA00033756507200000132
Figure FDA00033756507200000133
t is a total scheduling period;
uncertainty set of electric automobile running characteristics in discharging state
Figure FDA0003375650720000021
Comprises the following steps:
Figure FDA0003375650720000022
wherein the content of the first and second substances,
Figure FDA0003375650720000023
the total discharge power of the electric automobile in the discharge state at the moment t,
Figure FDA0003375650720000024
for the predicted discharge power of the electric vehicle in the discharge state at time t,
Figure FDA0003375650720000025
and
Figure FDA0003375650720000026
the maximum fluctuating discharge power of the electric automobile in the discharge state at the moment t respectively upwards and downwards,
Figure FDA0003375650720000027
and
Figure FDA0003375650720000028
all variables are 0 to 1,
Figure FDA0003375650720000029
Figure FDA00033756507200000210
Is the regulation coefficient of the electric automobile in the discharge state, and
Figure FDA00033756507200000211
step four: establishing a distributed robust optimization scheduling model under an uncertain set:
Figure FDA00033756507200000212
wherein the content of the first and second substances,
Figure FDA00033756507200000213
in order to reduce the running cost of the conventional unit,
Figure FDA00033756507200000214
for the output power of the ith conventional unit at time t,
Figure FDA00033756507200000215
and
Figure FDA00033756507200000216
starting and stopping state quantities of a conventional unit, respectively, when starting the conventional unit
Figure FDA00033756507200000217
When the conventional unit is stopped
Figure FDA00033756507200000218
In order to account for the fuel costs of the cogeneration unit,
Figure FDA00033756507200000219
is the power output value of the cogeneration unit,
Figure FDA00033756507200000220
in order to reduce the cost of the electric automobile,
Figure FDA00033756507200000221
and
Figure FDA00033756507200000222
charging power and discharging power respectively for the nth electric vehicle at time t, NGTotal number of conventional units, NCHPTotal number of cogeneration units, NEVIs the total number of the electric automobiles, P is the total indeterminate set of the electric heating combined system,
Figure FDA00033756507200000223
EP[·]for the expected value of any one of the distributions P,
Figure FDA00033756507200000224
wherein x is the output power adjustment value set of the conventional unit and the cogeneration unit,
Figure FDA00033756507200000225
a fluctuation value set C of wind power prediction error and electric vehicle charge and discharge powerEVRIn order to reduce the replacement cost of the battery of the electric automobile,
Figure FDA00033756507200000226
is the total charge and discharge capacity of the nth electric vehicle battery,
Figure FDA00033756507200000227
and
Figure FDA00033756507200000228
power fluctuation values of the electric vehicle in the charging state and the discharging state, cG,iAnd cCHP,iAdjusting cost coefficients for output power of the ith conventional unit and the ith cogeneration unit respectively,
Figure FDA00033756507200000229
and
Figure FDA00033756507200000230
the participation coefficients of the ith conventional unit and the ith cogeneration unit at the moment t respectively,
Figure FDA00033756507200000231
and
Figure FDA00033756507200000232
respectively the regulated power of the conventional unit and the cogeneration unit.
2. The electric-heat combined system distribution robust optimization scheduling method based on improved Wasserstein measure of claim 1, characterized in that power error data set is predicted according to historical wind power
Figure FDA0003375650720000031
Building an empirical distribution
Figure FDA0003375650720000032
Figure FDA0003375650720000033
Where N is the total number of historical samples, j is 1, 2., N,
Figure FDA00033756507200000315
predicting power error data for jth historical wind power
Figure FDA0003375650720000034
Dirac measure of.
3. The improved Wasserstein measure-based electric-thermal combined system distribution robust optimization scheduling method of claim 1 or 2, characterized in that the Euclidean norm is
Figure FDA0003375650720000035
The expression of (a) is as follows:
Figure FDA0003375650720000036
4. the improved Wasserstein measure-based robust optimization scheduling method for electric-thermal combined system distribution, according to claim 1, wherein the extreme scenarios of step two include the following two cases:
the first is that the wind power output power is the maximum value or the minimum value, and then the maximum wind power output power at the moment t
Figure FDA0003375650720000037
And minimum wind power output
Figure FDA0003375650720000038
The expression of (a) is:
Figure FDA0003375650720000039
wherein the content of the first and second substances,
Figure FDA00033756507200000310
the predicted value of the wind power output power at the moment t is obtained;
the second is that the climbing power of the wind power exceeds the threshold value, and the extreme climbing power of the wind power in the time interval (t, t + Δ t) is:
Figure FDA00033756507200000311
wherein the content of the first and second substances,
Figure FDA00033756507200000312
and
Figure FDA00033756507200000313
up and down power of wind power, P, respectivelyw,tAnd Pw,t+ΔtThe output power of the wind power is respectively at t moment and t + delta t moment, and delta t is time increment.
5. The electric-heat combined system distribution robust optimization scheduling method based on the improved Wasserstein measure of claim 1, wherein the electric vehicles with the state of charge of less than or equal to 20% are in a charging state, and the electric vehicles with the state of charge of more than or equal to 80% are in a discharging state.
6. The electric-heat combined system distribution robust optimization scheduling method based on improved Wasserstein measure according to claim 1, characterized in that the running cost of conventional units
Figure FDA00033756507200000314
Including fuel costs and start-stop costs.
CN202111417104.9A 2021-11-25 2021-11-25 Electric heating combined system distribution robust optimization scheduling method based on improved Wasserstein measure Pending CN113962612A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115688394A (en) * 2022-10-18 2023-02-03 上海科技大学 V2G distribution robust optimization method considering multiple uncertainties of power grid

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115688394A (en) * 2022-10-18 2023-02-03 上海科技大学 V2G distribution robust optimization method considering multiple uncertainties of power grid
CN115688394B (en) * 2022-10-18 2023-12-26 上海科技大学 V2G distribution robust optimization method considering multiple uncertainties of power grid

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